I'll have to go against the grain and say that Rurouni Kenshin left me cold. The first five episodes became very predictable to me, and I wasn't terribly interested in the story. From what I hear, the pattern continues on further on down the line, so I didn't really get into it.
Series I would highly recommend:
Trigun: Alternately funny and tragic, it's a show with a wonderful story and interesting cast.
Rahxepon: Kind of like Evangelion, if it was a LOT more fun. Very pretty, too.
Nadeisco: The king of anime that deconstructs anime. Many in-jokes, extremely silly at times (such that it has a hard time packing a punch when it tries to be serious) and an english dub that actually captures the zany nature of the dialogue.
Vandread: Amusing sexual politics, outstanding Gonzo CGI, and an inspired plot make for one of the most fun series around. A sexy exterior covers up a suprisingly deep set of characters. The kind of show I can watch over and over.
ANYTHING BY HAYAO MIYAZAKI: Be it Castle Cagliostro or Spirited Away, each film his hand has touched is gold. Truely one of the great Sensei's of anime, and a man who understands the difference between childish and child-like.
Ushio and Tora: For some reason it never caught on as big in the states as I expected, the tale of a boy and his captive demon is pretty amusing.
Cowboy Bebop: The anime you can show non-anime fans, and they'll enjoy. It's cool, it's hip and it's got some of the best writing in anime. You'd be doing yourself a disservice to miss it.
Giant Robo: The first of the 'remake' animes of recent years, and still the king. Giant robots in battle! Superheroes going toe to toe! The world in peril from it's greatest asset! A twisty-plot that tricks you left and right! This is the stuff, baby.
Big O: New School giant robots. Deep mystery, a noir attitude and fun Fun FUN! And the sequel's gonna be here soon.
How's that for starters? You want more? I got a ton.
